Caching Content under Digital Rights Management

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Caching Content under Digital Rights Management

• Leah Epstein, Amos Fiat and Meital Levy

University of Haifa Tel-Aviv
University Israel
Israel
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Problem Setting - informal
Files of different size and cost appear online.
The user purchases packages of files and needs to
evict cached files when the device runs out of
memory.
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Typical restrictions

• Usage restrictions included within various DRM
  packages include the following (a very partial
  list of possible restrictions supported or
  intended)
• Limited download ability.
• Some price p for a single download.
• Some other price q gtgt p for unlimited downloads.
• Limited use ability. The content may be
  downloaded for a pre-determined number of uses or
  a pre-determined length of time (e.g., NetFlix).

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Example
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Example Cont

• Consider the following sequence of requested
  movies Grease, Rambo, Forrest Gump, Rambo .
• The sequence contains 3 movies of different
  packages and sizes and a cache of size 6.

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Example Cont
Rambo (3), Purchase package p2 (unlimited, 10)
Grease (2), Purchase package p5 (single use,
2)
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Example Cont
Forrest Gump (5), Purchase package p3 (2 uses,
1), evict Grease and Rambo from the cache

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Example Cont
Rambo, No need to purchase a package, evict
Forrest Gump from the cache If Grease is
required again, a new package must be bought

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The general case

• The cache has size k
• Items are denoted by 1,2,,n
• Each item has a size associated with it
• Every item has a set of packages
• Every package has three attributes
• Initial cost
• Can be zero or positive
• Cost per download
• Can be zero or positive
• Maximum number of downloads
• can be finite or infinite

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The online problem

• Requests for items are presented one by one
• A request for an item arrives together with its
  list of packages
• To satisfy a request, if it is not in the cache,
  it must be downloaded into the cache
• Possibly evicting other requests to create space
• It can be downloaded using a previously bought
  package or a new one
• The cost of buying a package is paid if a package
  is bought
• The cost of download, if not zero, is paid

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Difficulties

• From the point of view of caching
• Eviction strategy which items to evict?
• From the point of view of generalized ski
  rental
• Purchase strategy which package to use?
• Commit on a package with a small average cost per
  download or
• Commit only on a small number of downloads

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Our Results

• Online caching of DRM controlled items is not
  much more difficult than the standard paging
  problem. O(k) competitive.
• The Diminishing Cost Landlord (DCLL)
  algorithm. A generalization of the standard
  Landlord Algorithm (Young, 1998).

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Simplifications

• There is no per-download cost in any package
• after the package has been purchased
• All costs are powers of 2
• If the cheapest package has cost C, then all
  costs 2C, 4C, 8C, exist
• Package offerings are Pareto-optimal
• The average cost on a single download does not
  increase with the size of packages
• The simplifications can be removed and yet
  increase the competitive ratio by at most a
  constant multiplicative factor

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The DRM algorithm

• The online DRM algorithm combines two components
• Purchasing strategy
• Eviction strategy (DCLL algorithm)
• The DRM caching algorithm simulates a diminishing
  cost landlord algorithm, DCLL.
• The DRM algorithm does an on-the-fly
  transformation of its own request sequence, to a
  sequence of events for the DCLL algorithm, by
  injecting file cost updates into the DCLL event
  sequence.

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File caching

• A cache of size k
• A sequence of requests for files arrives online
• A file has a size and a weight
• If not present in the cache, it must be inserted
  to the cache
• Possibly removing other files to make room for it
• The weight is the cost of bringing it into the
  cache

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Diminishing cost Landlord - DCLL

• The Diminishing Cost Landlord algorithm deals
  with the general case of standard caching where
  each file has an arbitrary cost and an arbitrary
  size, similarly to the landlord algorithm.
• Moreover, the algorithm can handle a special type
  of request called decrease cost" request. In
  this request, the cost/weight of the file drops
  for future requests for the file.
• The algorithm has a competitive ratio of k
• identical to the landlord algorithm.
• The proof is done with the same potential
  function used in the proof of the Landlord
  algorithm with additional cases.

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The Purchasing Strategy
On the first request to an item, purchase the
cheapest possible package for that item. When
all allowable downloads are used up, purchase the
next more expensive package, which is always
exactly twice as expensive. This algorithm is 2
competitive compared to the cost of an algorithm
which performs exactly the same operations on the
cache, but chooses packages in an optimal way.
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Sequence modification
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Relation between the sequences

• The entire cheapest package is charged to the
  first request
• Every package is charged strictly before it
  starts being used
• Conclusions from the DCLL cost sequence
  construction.
• At any point in time the accumulated cost for DRM
  on the original sequence is at most the
  accumulated cost of DCLL on modified sequence.
  Therefore the cost of the DRM algorithm is at
  most the cost of the DCLL algorithm
• At any point in time the accumulated cost for
  DCLL on the modified sequence is at most 3 times
  the accumulated cost of DRM on the original
  sequence. Therefore the cost for the DCLL
  algorithm is at most three times the cost of the
  DRM algorithm

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Analysis of the DRM algorithm

• The actual cost of the DRM algorithm does not
  exceed the cost charged by the DCLL algorithm.
  (Proved in previous slides)
• The cost charged to the DCLL adversary does not
  exceed O(1) times the cost charged to the DRM
  adversary.
• Given that the DCLL algorithm is O(k) competitive
  with respect to the DCLL adversary, this gives an
  O(k) competitive algorithm for DRM
• DRM ?O(1) DCLL ? O(k) OPTDCLL ? O(k) OPTDRM

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Analysis of the DRM algorithm

• 2. The cost charged to the DCLL adversary is at
  most O(1) times the cost charged to the DRM
  adversary.
• Proof
• Consider an optimal offline algorithm, A, for
  the DRM problem.
• The costs associated with an algorithm depend
  only on the number of faults this algorithm has
  on each item.
• Once this is set, the best package or collection
  of packages can be determined.
• Algorithm A for DRM induces an algorithm B for
  the DCLL setting with the same eviction policy.
• The cost of a fault for B is different and is
  based on modified costs

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• Given algorithm A for DRM
• Create an algorithm A for DRM, which uses the
  purchase policy as our algorithm
• Starts with the cheapest package and keeps buying
  a package which is twice is expensive
• The cost of A compared to A increases by a
  factor of 2
• Now compare A to B
• The comparison is similar to the analysis of the
  online algorithm
• As we saw, the cost of the modified sequence is
  at most 3 times the cost of the DRM sequence

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• Thank you